lddaly's method works, As does the below. You can 'fake out' the cache by adding an argument to the request, so the cache thinks it's a CGI generated image, so doesn't cache it.
In ajax-dashboard6.php, change <img id="RainGraph" src="<?php echo $RainGraphImage ?>" width='178' alt="rain graph" />
to <img id="RainGraph" src="<?php echo $RainGraphImage.'?t='.time(); ?>" width='178' alt="rain graph" />
and change <img style="width:80px; margin-left:auto; margin-right:auto" src="cache/heavenpie.png" alt="graph" width="80px" height="80px" id="HeavenPie"/>
to <img style="width:80px; margin-left:auto; margin-right:auto" src="cache/heavenpie.png<?php echo '?t='.time(); ?>" alt="graph" width="80px" height="80px" id="HeavenPie"/>